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United States Patent |
5,751,241
|
Lewiner
,   et al.
|
May 12, 1998
|
Method and apparatus for measuring the speed of a moving body
Abstract
To measure the speed of a body (1) moving relative to the ground (2) by
means of a broad-band Doppler radar (3) fixed to the moving body, two
incident radar waves are transmitted successively towards the ground at
instants that are close together, and the corresponding reflected waves
are picked up, the frequency of at least the first incident wave being
time-varying, the signals representative of the first incident and
reflected waves are multiplied together, a spectrum is determined for the
low frequency component of the product of said two signals, the same
operations are performed for second incident and reflected waves, then two
peaks that correspond with a certain amount of frequency shift in the two
spectra are identified, and the speed of the moving body is determined as
a function of the frequencies of these two singular points and as a
function of the height of the radar relative to the ground.
Inventors:
|
Lewiner; Jacques (7, avenue de Suresnes, 92210 Saint-Cloud, FR);
Carreel; Eric (9, rue de General Gouraud, 92190 Meudon, FR)
|
Appl. No.:
|
765285 |
Filed:
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March 10, 1997 |
PCT Filed:
|
June 30, 1995
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PCT NO:
|
PCT/FR95/00879
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371 Date:
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March 10, 1997
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102(e) Date:
|
March 10, 1997
|
PCT PUB.NO.:
|
WO96/01435 |
PCT PUB. Date:
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January 18, 1996 |
Foreign Application Priority Data
Current U.S. Class: |
342/104; 342/111; 342/112; 342/115; 342/116; 342/196 |
Intern'l Class: |
G01S 013/60 |
Field of Search: |
342/104,109,111,112,115,117,116,196,192
|
References Cited
U.S. Patent Documents
4302758 | Nov., 1981 | Tomasi | 343/9.
|
Foreign Patent Documents |
0 534 056 A1 | May., 1992 | EP.
| |
0 534 056 B1 | Mar., 1993 | EP.
| |
2 443 070 | Jun., 1980 | FR.
| |
Other References
French Search Report dated 20 Mar. 1995, French Appl. No. FR9408346
|
Primary Examiner: Sotomayor; John B.
Attorney, Agent or Firm: Marshall, O'Toole, Gerstein, Murray & Borun
Claims
We claim:
1. A method of measuring the speed v of a body moving in a direction
parallel to the ground, said measurement being performed by means of a
Doppler radar having a transmitter/receiver fixed to the moving body at a
certain height h above the ground and designed to transmit a radar beam
towards the ground along a mean axis extending forwards or backwards
relative to the direction of movement, said method including the following
steps:
a) at a first instant t.sub.1, supplying the radar transmitter/receiver
with a first sinusoidal control electrical signal at a first frequency
f.sub.1 to cause the transmitter/receiver to transmit a first incident
radar wave at the same frequency f.sub.1 ;
b) receiving a first reflected radar wave generated by the first incident
radar wave being reflected on the ground, and generating from said first
reflected radar wave a first received electrical signal;
c) multiplying together the first control electrical signal and the first
received electrical signal, thereby generating a first multiplied
electrical signal having a high frequency component and a low frequency
component;
d) filtering the first multiplied electrical signal to generate a first
filtered signal proportional to the low frequency component of the first
multiplied signal; and
e) during a first measurement time .DELTA.t.sub.1 starting at the first
instant t.sub.1, determining a first frequency spectrum corresponding to
the first filtered signal;
wherein the transmitted radar beam is relatively broad, wherein the first
frequency f.sub.1 is time-varying, and wherein said method further
includes the following steps:
f) measuring the height h of the radar transmitter/receiver above the
ground;
g) at a second instant t.sub.2 very close to the first instant t.sub.1,
supplying the transmitter/receiver with a second sinusoidal control
electrical signal having a second frequency f.sub.2 to cause the
transmitter/receiver to transmit a second incident radar wave at that same
frequency f.sub.2 ;
h) receiving a second reflected radar wave generated by reflection of the
second incident radar wave on the ground, and generating a second received
electrical signal from said second reflected radar wave;
i) multiplying together the second control electrical signal and the second
received electrical signal, thereby generating a second multiplied
electrical signal having a high frequency component and a low frequency
component;
j) filtering the second multiplied electrical signal to generate a second
filtered signal proportional to the low frequency component of the second
multiplied signal;
k) during a second measurement time .DELTA.t.sub.2 starting from the second
instant t.sub.2, determining a second frequency spectrum corresponding to
the second filtered signal;
l) identifying a first singular point in the first spectrum and a second
singular point in the second spectrum such that the first and second
spectra in the vicinity of said two singular points are similar in form
but with a certain frequency shift, said two singular points being
generated by reflection from the same point on the ground;
m) measuring in the first and second spectra first and second frequencies
F.sub.1, F.sub.2 corresponding respectively to the first and second
singular points; and
n) computing the speed v of the moving body relative to the ground on the
basis of the height h of the radar transmitter/receiver above the ground
and of the first and second frequencies F.sub.1, F.sub.2 corresponding to
the two singular points.
2. A method according to claim 1, in which:
the first and second frequencies f.sub.1, f.sub.2 are linear functions of
time, at least during the first and second measurement times
.DELTA.t.sub.1, .DELTA.t.sub.2 ; and
step n) consists in solving the following system of two equations in two
unknowns .alpha. and v:
##EQU19##
where: c is the propagation speed of the radar wave in air;
.alpha. is the angle between the direction in which the body is moving and
a direction extending between the transmitter/receiver and the point on
the ground that has generated the first and second singular points;
f.sub.1 (t.sub.1 +.DELTA.t.sub.1 /2) designates the value of the first
frequency f.sub.1 at instant t.sub.1 +.DELTA.t.sub.1 /2;
f.sub.1 ' designates the value of the time derivative of the first
frequency f.sub.1 during the first measurement time .DELTA.t.sub.1 ;
f.sub.2 (t.sub.2 +.DELTA.t.sub.2 /2) designates the value of the second
frequency f.sub.2 at instant t.sub.2 +.DELTA.t.sub.2 /2; and
f.sub.2 ' designates the value of the time derivative of the second
frequency f.sub.2 during the second measurement time .DELTA.t.sub.2.
3. A method according to claim 2, in which the second frequency f.sub.2 is
constant, and the first frequency f.sub.1 at instant t.sub.1
+.DELTA.t.sub.1 /2 presents a value f.sub.1 (t.sub.1 +.DELTA.t.sub.1 /2)
close to that of the second frequency f.sub.2, the speed v of the moving
body relative to the ground then being computed from the formula:
##EQU20##
4. A method according to claim 2, in which the radar beam includes a
transmission direction that is substantially perpendicular to the ground
such that the first spectrum includes a characteristic peak P.sub.1
(.pi./2) corresponding to said direction substantially perpendicular to
the ground, step f) of the method including a step that consists in
measuring a frequency F.sub.1 (.pi./2) corresponding to said
characteristic peak in the first spectrum followed by a step consisting in
computing the height h of the radar transmitter/receiver relative to the
ground from the formula:
##EQU21##
5. A method according to claim 1, in which steps e) and k) include a step
of digitizing the first and second filtered signals.
6. A method according to claim 5, in which the first and second spectra are
determined by the fast Fourier transform on the basis of the digitized
first and second filtered signals.
7. A method according to claim 1, in which steps l) and m) are performed
for a plurality of pairs of first and second singular points so as to
obtain a plurality of pairs of first and second frequencies F.sub.1,
F.sub.2 corresponding respectively to said pairs of singular points in the
first and second spectra, the speed v of the moving body then being
computed as a function of the height h of the radar transmitter/receiver
above the ground and of the various pairs of first and second frequencies
F.sub.1, F.sub.2 corresponding to the singular points.
8. A method according to claim 7, in which step f) consists in computing
the height h simultaneously as the speed v from the various pairs of first
and second frequencies F.sub.1, F.sub.2 corresponding to the singular
points.
9. A method according to claim 1, in which the moving body is a vehicle
running on the ground.
10. Apparatus for implementing a method according to claim 1 in order to
measure the speed v of a body moving in a direction parallel to the
ground, said apparatus comprising:
a radar wave transmitter/receiver, said transmitter/receiver having an
input for receiving a sinusoidal control electrical signal at a certain
frequency f.sub.1, f.sub.2 to generate an incident radar wave of the same
frequency by forming a radar beam directed towards the ground, going
forwards or backwards relative to the direction of movement, said
transmitter/receiver further including an output for generating a received
electrical signal from a reflected radar wave received by the
transmitter/receiver;
an oscillator including an output connected to the input of the
transmitter/receiver and designed to generate the control electrical
signal;
a mixer circuit having two inputs and an output, the two inputs of the
mixer being connected respectively to the output of the
transmitter/receiver and to the oscillator to receive respectively the
control electrical signal and the received electrical signal, the mixer
circuit generating at its output a multiplied electrical signal
corresponding to the product of the received electrical signal multiplied
by the control electrical signal, said multiplied signal having a high
frequency component and a low frequency component;
a lowpass filter having an input and an output, the input of the lowpass
filter being connected to the output of the mixer to receive the
multiplied signal, and the lowpass filter being designed to generate a
filtered signal at its output representative of the low frequency
component of the multiplied signal; and
a central unit including a first input connected to the output of the
lowpass filter to receive the filtered signal, said central unit being
designed to determine a frequency spectrum of the filtered signal in order
to compute the speed v of the moving body from the filtered signal;
wherein the beam of the incident radar wave is relatively broad, the
oscillator further including a control input designed to receive a control
voltage, the oscillator being designed so that the frequency of the
control electrical signal is a function of the control voltage, the
control input of the oscillator being connected to a voltage generator
itself driven by the central unit, the central unit further including
means for determining the height h of the transmitter/receiver relative to
the ground, and the central unit being designed:
to cause the voltage generator to generate in alternation a first control
voltage and a second control voltage so as to cause the oscillator to
generate in alternation first and second control electrical signals having
respective first and second frequencies f.sub.1, f.sub.2 respectively
proportional to the first and second control voltages, at least the first
control voltage being time-varying, so that at least the first frequency
f.sub.1 is time-varying;
during a first measurement time .DELTA.t.sub.1 starting from a first
instant t.sub.1, to determine a first frequency spectrum of the filtered
signal while the oscillator generates the first control electrical signal,
and during a second measurement time .DELTA.t.sub.2 starting from a second
instant t.sub.2 very close to the first instant t.sub.1, to determine a
second frequency spectrum of said filtered signal at a second instant
t.sub.2 very close to the first instant t.sub.1, during which the
oscillator generates the second control electrical signal;
to identify a first singular point in the first spectrum and a second
singular point in the second spectrum such that the first and second
spectra have forms that are similar in the vicinity of said two singular
points but with a certain frequency shift, said two singular points being
generated by reflection from the same point of the ground;
to measure first and second frequencies F.sub.1, F.sub.2 corresponding
respectively to the first and second singular points in the first and
second spectra; and
to compute the speed v of the moving body relative to the ground on the
basis of the height h of the radar transmitter/receiver above the ground
and of the first and second frequencies F.sub.1, F.sub.2 corresponding to
the two singular points.
11. Apparatus according to claim 10, in which:
the first and second frequencies f.sub.1, f.sub.2 are linear functions of
time, at least during the first and second measurement times
.DELTA.t.sub.1, .DELTA.t.sub.2 ; and
the central unit is designed to solve the following system of two equations
in two unknowns .alpha. and v:
##EQU22##
where: c is the propagation speed of the radar wave in air;
.alpha. is the angle between the direction in which the body is moving and
a direction extending between the transmitter/receiver and the point on
the ground that has generated the first and second singular points;
f.sub.1 (t.sub.1 +.DELTA.t.sub.1 /2) designates the value of the first
frequency f.sub.1 at instant t.sub.1 +.DELTA.t.sub.1 /2;
f.sub.1 ' designates the value of the time derivative of the first
frequency f.sub.1 during the first measurement time .DELTA.t.sub.1 ;
f.sub.2 (t.sub.2 +.DELTA.t.sub.2 /2) designates the value of the second
frequency f.sub.2 at instant t.sub.2 +.DELTA.t.sub.2 /2; and
f.sub.2 ' designates the value of the time derivative of the second
frequency f.sub.2 during the second measurement time .DELTA.t.sub.2.
12. Apparatus according to claim 10, in which the central unit includes a
second input connected to a height sensor to receive a signal
representative of the height h of the transmitter/receiver relative to the
ground, said second input constituting the above-mentioned means of the
central unit for determining the height h of the transmitter/receiver
relative to the ground.
13. Apparatus according to claim 10, in which the beam of the incident
radar wave includes a transmission direction that is substantially
perpendicular to the ground, such that the first spectrum includes a peak
characteristic of said direction that is substantially perpendicular to
the ground, the means for determining the height h of the
transmitter/receiver relative to the ground comprising means for measuring
a frequency F.sub.1 (.pi./2) corresponding to said characteristic peak and
means for computing said height h from said frequency F.sub.1 (.pi./2).
14. Apparatus according to claim 10, in which the control unit is designed
to digitize the filtered signal it receives at its first input prior to
determining the frequency spectrum of said filtered signal.
Description
FIELD OF THE INVENTION
The invention relates to methods for measuring the speed of a moving body,
and to apparatuses for implementing said methods.
BACKGROUND OF THE INVENTION
More particularly, the invention relates to a method of measuring the speed
v of a body, in particular a vehicle, moving in a direction parallel to
the ground, said measurement being performed by means of a Doppler radar
having a transmitter/receiver fixed to the moving body at a certain height
h above the ground and designed to transmit a radar beam towards the
ground along a mean axis extending forwards or backwards relative to the
direction of movement, said method including the following steps:
a) at a first instant t.sub.1, supplying the radar transmitter/receiver
with a first sinusoidal control electrical signal at a first frequency
f.sub.1 to cause the transmitter/receiver to transmit a first incident
radar wave at the same frequency f.sub.1 ;
b) receiving a first reflected radar wave generated by the first incident
radar wave being reflected on the ground, and generating from said first
reflected radar wave a first received electrical signal;
c) multiplying together the first control electrical signal and the first
received electrical signal, thereby generating a first multiplied
electrical signal having a high frequency component and a low frequency
component;
d) filtering the first multiplied electrical signal to generate a first
filtered signal proportional to the low frequency component of the first
multiplied signal; and
e) during a first measurement time .DELTA.t.sub.1 starting at the first
instant t.sub.1, determining a first frequency spectrum corresponding to
the first filtered signal.
Document EP-A-0 534 056 describes one example of such a method.
That mode of measurement is more accurate than using conventional
revolution counters or angle sensors which measure the speed of rotation
of the wheels of the vehicle, insofar as variations in wheel diameter and
the wheels slipping or skidding on the ground give rise to relatively
large errors in speeds measured by means of revolution counters or the
like.
In addition, the Doppler effect radar merely needs to be fixed to the
structure of the vehicle, and is simpler to install than a revolution
counter which implies a mechanism connected to the moving parts of the
wheels.
In known methods of the kind in question, the frequency spectrum of the
filtered signal has a peak corresponding to a certain frequency, and that
frequency can be used to compute the speed of the moving body relative to
the ground, given an angle .alpha. formed between the travel direction of
the moving body and the transmit-and-receive direction of the radar wave
relative to the transmitter/receiver.
If the selected angle .alpha. is 90.degree., then the transmitted wave is
indeed reflected by the ground, even if the ground presents no particular
irregularity, but in this case the frequency shift due to the Doppler
effect is nil.
In contrast, if the angle .alpha. is small relative to 90.degree., the
frequency shift due to the Doppler effect is large, providing it is
possible to receive a reflected wave from ground roughnesses extending
perpendicularly to the reflected wave.
The frequency spectrum of the first filtered signal therefore depends
strongly on the angle .alpha..
For that angle to be well defined, it is necessary for the radar beam to be
very narrow, so that known methods of the kind in question operate poorly
when the body is moving over relatively smooth ground, as applies for
example to a road surface, particularly in the event of rain or ice.
Because the radar beam is narrow, there is then low probability of the beam
encountering a reflecting obstacle capable of returning a reflected wave
to the transmitter/receiver to enable the speed of the moving body to be
measured.
In addition, if the beam is highly directional, then it is necessary to use
a transmit-and-receive antenna that is directional, which antenna must
therefore have lateral dimensions that are large relative to the
wavelength used, and that constitutes a handicap both in terms of cost and
in terms of ease of implementation.
Also, known methods of the kind in question generate measurement errors
when the above-mentioned .alpha. varies unintentionally, e.g. when the
moving body is a vehicle that is tilted forwards or backwards to a greater
or lesser extent depending on its loading.
Also, document FR-A-2 443 070 describes a method of measuring the speed of
an airplane relative to the ground by transmitting two radar waves in turn
to the ground at different varying frequencies. That method, which does
not involve determining the frequency spectrum of the low frequency
component of the multiplied signal, makes use of an iterative technique
enabling two particular angles of incidence .alpha.1 and .alpha.2 to be
determined which correspond respectively to the minimum beat frequency
values of the two radar waves, where the beat frequency is the frequency
of the low frequency component of the above-mentioned multiplied signal.
That method is therefore effective only so long as there exists a
reflected radar wave for the above-mentioned particular angles of
incidence .alpha.1 and .alpha.2: it therefore suffers from the same
drawbacks as the above-mentioned method which uses a narrow radar beam.
OBJECT AND BRIEF SUMMARY OF THE INVENTION
A particular aim of the present invention is to remedy those drawbacks.
To this end, according to the invention, in a method of the kind in
question including frequency spectrum determination the transmitted radar
beam is relatively broad, the first frequency f.sub.1 is time-varying, and
said method further includes the following steps:
f) measuring the height h of the radar transmitter/receiver above the
ground;
g) at a second instant t.sub.2 very close to the first instant t.sub.1,
supplying the transmitter/receiver with a second sinusoidal control
electrical signal having a second frequency f.sub.2 to cause the
transmitter/receiver to transmit a second incident radar wave at that same
frequency f.sub.2 ;
h) receiving a second reflected radar wave generated by reflection of the
second incident radar wave on the ground, and generating a second received
electrical signal from said second reflected radar wave;
i) multiplying together the second control electrical signal and the second
received electrical signal, thereby generating a second multiplied
electrical signal having a high frequency component and a low frequency
component;
j) filtering the second multiplied electrical signal to generate a second
filtered signal proportional to the low frequency component of the second
multiplied signal;
k) during a second measurement time .DELTA.t.sub.2 starting from the second
instant t.sub.2, determining a second frequency spectrum corresponding to
the second filtered signal;
l) identifying a first singular point in the first spectrum and a second
singular point in the second spectrum such that the first and second
spectra in the vicinity of said two singular points are similar in form
but with a certain frequency shift, said two singular points being
generated by reflection from the same point on the ground;
m) measuring, in the first and second spectra, first and second frequencies
F.sub.1, F.sub.2 corresponding respectively to the first and second
singular points; and
n) computing the speed v of the moving body relative to the ground on the
basis of the height h of the radar transmitter/receiver above the ground
and of the first and second frequencies F.sub.1, F.sub.2 corresponding to
the two singular points.
Thus, because a broad radar beam is used, there is a high chance that each
transmitted radar wave will encounter a reflecting obstacle on the ground
and will therefore be accompanied by a reflection back to the radar
transmitter receiver such that there always exist at least a portion of
the first and second frequency spectra usable for computing the speed of
the moving body by the Doppler effect.
Also, variations in the angle a can be ignored since the two Doppler
measurements performed make it possible to compute simultaneously both the
angle .alpha. and the speed v: in other words, it is possible to provide
an expression for the speed v that is independent of the angle .alpha..
In preferred implementations of the method of the invention, use is also
made of one or more of the following dispositions:
the first and second frequencies f.sub.1, f.sub.2 are linear functions of
time, at least during the first and second measurement times
.DELTA.t.sub.1, .DELTA.t.sub.2 ; and step n) consists in solving the
following system of two equations in two unknowns .alpha. and v:
##EQU1##
where: the symbols .vertline..vertline. on either side of an expression
designate the absolute value of the expression, here and throughout the
present text;
c is the propagation speed of the radar wave in air;
.alpha. is the angle between the direction in which the body is moving and
a direction extending between the transmitter/receiver and the point on
the ground that has generated the first and second singular points;
f.sub.1 (t.sub.1 +.DELTA.t.sub.1 /2) designates the value of the first
frequency f.sub.1 at instant t.sub.1 +.DELTA.t.sub.1 /2;
f.sub.1 ' designates the value of the time derivative of the first
frequency f.sub.1 during the first measurement time .DELTA.t.sub.1 ;
f.sub.2 (t.sub.2 +.DELTA.t.sub.2 /2) designates the value of the second
frequency f.sub.2 at instant t.sub.2 +.DELTA.t.sub.2 /2; and
f.sub.2 ' designates the value of the time derivative of the second
frequency f.sub.2 during the second measurement time .DELTA.t.sub.2 ;
the second frequency f.sub.2 is constant, and the first frequency f.sub.1
at instant t.sub.1 +.DELTA.t.sub.1 /2 presents a value f.sub.1 (t.sub.1
+.DELTA.t.sub.1 /2) close to that of the second frequency f.sub.2, the
speed v of the moving body relative to the ground then being computed from
the formula:
##EQU2##
thus enabling the speed to be determined particularly simply; the radar
beam includes a transmission direction that is substantially perpendicular
to the ground such that the first spectrum includes a characteristic peak
P.sub.1 (.pi./2) corresponding to said direction substantially
perpendicular to the ground, the method including a step that consists in
measuring a frequency F.sub.1 (.pi./2) corresponding to said
characteristic peak in the first spectrum followed by a step consisting in
computing the height h of the radar transmitter/receiver relative to the
ground from the formula:
##EQU3##
thus avoiding any need for an additional sensor to measure the height h;
steps e) and k) include a step of digitizing the first and second filtered
signals, thus enabling the spectrum to be determined in particularly
simple manner;
the first and second spectra are determined by the fast Fourier transform
on the basis of the digitized first and second filtered signals;
steps l) and m) are performed for a plurality of pairs of first and second
singular points so as to obtain a plurality of pairs of first and second
frequencies F.sub.1, F.sub.2 corresponding respectively to said pairs of
singular points in the first and second spectra, the speed v of the moving
body then being computed as a function of the height h of the radar
transmitter/receiver above the ground and of the various pairs of first
and second frequencies F.sub.1, F.sub.2 corresponding to the singular
points;
step f) consists in computing the height h simultaneously as the speed v
from the various pairs of first and second frequencies F.sub.1, F.sub.2
corresponding to the singular points; and
the moving body is a vehicle running on the ground.
The invention also provides apparatus for implementing a method as defined
above, the apparatus comprising:
a radar wave transmitter/receiver, said transmitter/receiver having an
input for receiving a sinusoidal control electrical signal at a certain
frequency f.sub.1, f.sub.2 to generate an incident radar wave of the same
frequency by forming a radar beam directed towards the ground, going
forwards or backwards relative to the direction of movement, said
transmitter/receiver further including an output for generating a received
electrical signal from a reflected radar wave received by the
transmitter/receiver;
an oscillator including an output connected to the input of the
transmitter/receiver and designed to generate the control electrical
signal;
a mixer circuit having two inputs and an output, the two inputs of the
mixer being connected respectively to the output of the
transmitter/receiver and to the oscillator to receive respectively the
control electrical signal and the received electrical signal, the mixer
circuit generating at its output a "multiplied" electrical signal
corresponding to the product of the received electrical signal multiplied
by the control electrical signal, said multiplied signal having a high
frequency component and a low frequency component;
a lowpass filter having an input and an output, the input of the lowpass
filter being connected to the output of the mixer to receive the
multiplied signal, and the lowpass filter being designed to generate a
filtered signal at its output representative of the low frequency
component of the multiplied signal; and
a central unit including a first input connected to the output of the
lowpass filter to receive the filtered signal, said central unit being
designed to determine a frequency spectrum of the filtered signal in order
to compute the speed v of the moving body from the filtered signal;
the apparatus being wherein the beam of the incident radar wave is
relatively broad, the oscillator further including a control input
designed to receive a control voltage, the oscillator being designed so
that the frequency of the control electrical signal is a function of the
control voltage, the control input of the oscillator being connected to a
voltage generator itself driven by the central unit, the central unit
further including means for determining the height h of the
transmitter/receiver relative to the ground, and the central unit being
designed:
to cause the voltage generator to generate in alternation a first control
voltage and a second control voltage so as to cause the oscillator to
generate in alternation first and second control electrical signals having
respective first and second frequencies f.sub.1, f.sub.2 respectively
proportional to the first and second control voltages, at least the first
control voltage being time-varying, so that at least the first frequency
f.sub.1 is time-varying;
during a first measurement time .DELTA.t.sub.1 starting from a first
instant t.sub.1, to determine a first frequency spectrum of the filtered
signal while the oscillator generates the first control electrical signal,
and during a second measurement time .DELTA.t.sub.2 starting from a second
instant t.sub.2 very close to the first instant t.sub.1, to determine a
second frequency spectrum of said filtered signal at a second instant
t.sub.2 very close to the first instant t.sub.1, during which the
oscillator generates the second control electrical signal;
to identify a first singular point in the first spectrum and a second
singular point in the second spectrum such that the first and second
spectra have forms that are similar in the vicinity of said two singular
points but with a certain frequency shift, said two singular points being
generated by reflection from the same point of the ground;
to measure first and second frequencies F.sub.1, F.sub.2 corresponding
respectively to the first and second singular points in the first and
second spectra; and
to compute the speed v of the moving body relative to the ground on the
basis of the height h of the radar transmitter/receiver above the ground
and of the first and second frequencies F.sub.1, F.sub.2 corresponding to
the two singular points.
In preferred embodiments of the apparatus of the invention, use is also
made of one or more of the following dispositions:
the first and second frequencies f.sub.1, f.sub.2 are linear functions of
time, at least during the first and second measurement times
.DELTA.t.sub.1, .DELTA.t.sub.2, and the central unit is designed to solve
the following system of two equations in two unknowns .alpha. and v:
##EQU4##
where: c is the propagation speed of the radar wave in air;
.alpha. is the angle between the direction in which the body is moving and
a direction extending between the transmitter/receiver and the point on
the ground that has generated the first and second singular points;
f.sub.1 (t.sub.1 +.DELTA.t.sub.1 /2) designates the value of the first
frequency f.sub.1 at instant t.sub.1 +.DELTA.t.sub.1 /2;
f.sub.1 ' designates the value of the time derivative of the first
frequency f.sub.1 during the first measurement time .DELTA.t.sub.1 ;
f.sub.2 (t.sub.2 +.DELTA.t.sub.2 /2) designates the value of the second
frequency f.sub.2 at instant t.sub.2 +.DELTA.t.sub.2 /2; and
f.sub.2 ' designates the value of the time derivative of the second
frequency f.sub.2 during the second measurement time .DELTA.t.sub.2 ;
the central unit includes a second input connected to a height sensor to
receive a signal representative of the height h of the
transmitter/receiver relative to the ground, said second input
constituting the above-mentioned means of the central unit for determining
the height h of the transmitter/receiver relative to the ground;
the beam of the incident radar wave includes a transmission direction that
is substantially perpendicular to the ground, such that the first spectrum
includes a peak characteristic of said direction that is substantially
perpendicular to the ground, the means for determining the height h of the
transmitter/receiver relative to the ground comprising means for measuring
a frequency F.sub.1 (.pi./2) corresponding to said characteristic peak and
means for computing said height h from said frequency F.sub.1 (.pi./2);
and
the control unit is designed to digitize the filtered signal it receives at
its first input prior to determining the frequency spectrum of said
filtered signal.
BRIEF DESCRIPTION OF THE DRAWING
Other characteristics and advantages of the invention appear from the
following detailed description of an embodiment thereof, given by way of
non-limiting example and with reference to the accompanying drawing.
In the drawing:
FIG. 1 is a diagrammatic overall view of a vehicle fitted with
speed-measuring radar constituting an embodiment of the invention;
FIG. 2 is a block diagram of the radar of the FIG. 1 vehicle;
FIG. 3 is a spectrum diagram showing one example of frequency variation in
the wave transmitted by the radar of FIG. 2; and
FIG. 4 shows two frequency spectra of a signal output by the lowpass filter
9 of FIG. 2, determined at two different instants that are very close
together.
MORE DETAILED DESCRIPTION
As shown diagrammatically in FIG. 1, the invention seeks to determine the
speed v of a moving body 1, in particular a motor vehicle running on
ground 2, with the measurement being performed by means of a Doppler
effect radar 3 which transmits an incident radar beam 4 towards the ground
in a forwards or backwards direction, the incident beam being relatively
broad, e.g. having a divergence angle of about 45.degree..
The speed as measured by the radar 3 can be applied to a display device la
on the vehicle dashboard, or to any other member of the vehicle, e.g. an
anti-lock braking system for the wheels.
As shown diagrammatically in FIG. 2, the radar 3 may comprise:
a radar wave transmitter/receiver 5 having an input 5a for receiving a
sinusoidal control electrical signal so as to generate an incident radar
wave at the same frequency as the signal to constitute the incident radar
beam 4, said transmitter/receiver also including an output 5b for
generating a received electrical signal on reception of a radar wave
reflected by the ground 2 from the incident wave;
a voltage-controlled oscillator 6 having an output 6a connected to the
input 5a of the transmitter/receiver and an input 6b for receiving a
control voltage, the output 6a being designed to generate said control
electrical signal at a frequency f.sub.1, f.sub.2 depending on the control
voltage;
a voltage generator 7 having an output 7a for generating said control
voltage and a logic input 7b for driving the control voltage;
a mixer circuit 8 having two inputs 8a and 8b and an output 8c, the input
8a of the mixer being connected to the output 5b of the
transmitter/receiver and the input 8b of the mixer being connected to the
output 6a of the oscillator or possibly to an additional output 6c of said
oscillator at which an electrical signal is generated that is proportional
to the control electrical signal but of lower power, the mixer circuit 8
being deigned to generate a "multiplied" electrical signal at its output
8c and corresponding to the product of the received electrical signal
multiplied by the control electrical signal, said multiplied signal having
a high frequency component and a low frequency component;
a lowpass filter 9 having an input 9a which is connected to the output 8c
of the mixer, and an output 9b at which a filtered signal is generated
representative of the low frequency component of the multiplied signal;
and
a central unit 10 having a first input 10a connected to the output 9b of
the lowpass filter to receive the filtered signal, a second input 10b
connected to a height sensor 11, e.g. an ultrasound or other sensor for
the purpose of receiving a signal representative of the height h of the
transmitter/receiver 5 relative to the ground 2, said height h being
measured perpendicularly to the ground, and the central unit further
including a first output 10c connected to the logic input 7b of the
voltage generator 7 to drive said voltage generator, and a second output
10d connected to the display 1a or to some other member.
The central unit 10 is programmed:
to cause the voltage generator 7 to generate in alternation a first control
voltage that is time-varying and a second control voltage that is constant
or varying, so as to cause the oscillator to generate in alternation first
and second control electrical signals Ec.sub.1 and Ec.sub.2 having the
first and second frequencies f.sub.1 and f.sub.2 respectively, which
frequencies are respectively proportional to the first and second control
voltages (for example, f.sub.1 may be constituted by a portion of a ramp
that increases linearly from a constant frequency f.sub.0 and then falls
back to f.sub.0, while f.sub.2 may be constituted by the constant
frequency f.sub.0, as shown in FIG. 3);
to determine a first frequency spectrum S.sub.1 of the filtered signal
during a first measurement time .DELTA.t.sub.1 starting from a first
instant t.sub.1 during which the oscillator generates the first control
electrical signal Ec.sub.1, and to determine a second frequency spectrum
S.sub.2 of the filtered signal during a second measurement time
.DELTA.t.sub.2 starting from a second instant t.sub.2 very close to the
first instant t.sub.1 (before or after the first instant t.sub.1), during
which the oscillator generates the second control electrical signal
Ec.sub.2 (see FIG. 4);
to identify a first peak P.sub.1 in the first spectrum S.sub.1, and a
second peak P.sub.2 in the second spectrum S.sub.2, such that the first
and second spectra are similar in form in the vicinity of said two peaks
but with a certain frequency shift, said two peaks then being generated by
a reflection from the same reflecting point 2a on the ground, said point
generally corresponding to an irregularity of the ground;
to measure the first and second frequencies F.sub.1 and F.sub.2
corresponding respectively to the first and second peaks P.sub.1 and
P.sub.2 in the first and second spectra S.sub.1 and S.sub.2 ; and
to compute the speed v of the moving body relative to the ground on the
basis of the height h of the radar transmitter/reciever above the ground,
and on the basis of the measured first and second frequencies F.sub.1 and
F.sub.2, the computation being performed as explained below.
In the vicinity of the first instant t.sub.1, the first control electrical
signal Ec.sub.1 can be expressed in the form:
Ec.sub.1 =A.sub.1 sin (2.pi.f.sub.1 (t.sub.1).multidot.t) (I)
where:
t represents time;
A.sub.1 is a constant; and
f.sub.1 (t.sub.1) represents the value of the first frequency f.sub.1 at
the first instant t.sub.1.
Under such conditions, the first received electrical signal Er.sub.1
corresponding to the first peak P.sub.1 is expressed as follows, in
application of the well-known Doppler shift formula:
##EQU5##
where: A.sub.2 is a constant;
.alpha. represents the angle between the displacement direction of the body
and the direction to the point 2a on the ground seen from the
transmitter/receiver 5 (.alpha. lying in the range 0 to .pi./2 radians if
the radar beam is directed forwards, and lying in the range .pi./2 and
.pi. if the beam is directed backwards); and
c represents the propagation speed of the radar wave in air.
The first received electrical signal Er.sub.1 is generated at the output 5b
of the transmitter/reciever 5 at an instant t.sub.1 +dt, where dt
corresponds to the go-and-return time for the electromagnetic wave between
the transmitter/receiver and the point 2a on the ground.
Consequently, the mixer circuit 8 generates a "multiplied" signal which is
the product of the first received electrical signal corresponding to above
formula (II) multiplied by the first control electrical signal, but with
said first control electrical signal then having a frequency f.sub.1
(t.sub.1 +dt), since said multiplication is performed at instant t.sub.1
+dt.
The "multiplied" signal generated at the output from the mixer corresponds
to the sum of two terms C.sub.1 and D.sub.1 given below in application of
conventional trigonometrical formulae:
##EQU6##
The term C.sub.1 is a high frequency signal while the term D.sub.1 is a low
frequency signal.
Only the low frequency signal D.sub.1 passes through the lowpass filter 9
to the first input 10a of the central unit 10. This low frequency signal
presents a frequency F.sub.1 corresponding to a peak P.sub.1 in the first
spectrum S.sub.1, i.e. corresponding to the reflection of the radar wave
on the reflecting point 2a.
If the first measurement time .DELTA.t.sub.1 were nil, then this frequency
would be expressed in the following form:
##EQU7##
where: .vertline..vertline. designates the absolute value function.
f.sub.1 is preferably a linear function of time, at least during the first
measurement time .DELTA.t.sub.1, such that:
f.sub.1 (t.sub.1 +dt)-f.sub.1 (t.sub.1)=f1'.multidot.dt
where f1' is the value of the time derivative of the first frequency
f.sub.1 during the first measurement time .DELTA.t.sub.1.
Also, account must be taken of the fact that the first measurement time
.DELTA.t.sub.1 is not nil, such that to a first approximation expression
(IV) can be written:
##EQU8##
Also, the time interval dt can be written in the form:
##EQU9##
whence
##EQU10##
Also, the incident radar wave corresponding to the second control
electrical signal Ec.sub.2 likewise generates a large reflection on point
2a of the ground, and because the second instant t.sub.2 is very close to
the first instant t.sub.1, the angle .alpha. between the travel direction
of the vehicle and the direction at which the point 2a is seen from the
transmitter/receiver 5 is substantially the same at both instants t.sub.1
and t.sub.2.
Under such conditions, and in the same manner as explained above, the
second spectrum S.sub.2 includes a peak P.sub.2 which corresponds to the
radar wave being reflected on the point 2a, said peak P.sub.2
corresponding to a frequency F.sub.2 that is expressed as follows:
##EQU11##
where f.sub.2 (t.sub.2 +.DELTA.t.sub.2 /2) is the value of the second
frequency f.sub.2 at the instant t.sub.2 +.DELTA.t.sub.2 /2;
f.sub.2 ' is the value of the time derivative of the second frequency
f.sub.2 during the second measurement time .DELTA.t.sub.2.
Thus, the central unit 10 can determine the speed v of the vehicle by
solving the system of two equations (VII) and (VIII) in two unknowns
.alpha. and v, the other parameters of these two equations all being known
to the central unit 10.
The system of equations (VII) and (VIII) can thus be written:
##EQU12##
where: a.sub.1, b.sub.1, a.sub.2, and b.sub.2 are known parameters, said
system of equations reducing to:
##EQU13##
given that cos.sup.2 .alpha.+ sin.sup.2 .alpha.1.
The second frequency f.sub.2 may possibly be constant, as shown in FIG. 3,
in which case the frequency F.sub.2 of the second peak P.sub.2 corresponds
to the following expression:
##EQU14##
If the values f.sub.1 (t.sub.1 +.DELTA.t.sub.1 /2) and f.sub.2 are very
close, as shown in FIG. 3, it is then possible from formulae (XI) and
(VII) and also taking account of the fact that the expression giving the
absolute value of F.sub.1 has the same sign as its term in (2v.cos
.alpha.)/c for usual values of h, v, and .alpha.:
##EQU15##
from which it results that
##EQU16##
The value of the speed v thus corresponds to the following expression:
##EQU17##
In a special case where f.sub.1 and f.sub.2 are such as shown in FIG. 3,
where f.sub.1 is a linear function of time having a slope of 1 GHz/s,
where f.sub.2 has a constant value f.sub.2, e.g. equal to 24 GHz, where
f.sub.2 (t.sub.2)=f.sub.1 (t.sub.1), the second frequency F.sub.2 of the
second peak P.sub.2 will be 2376 Hz for an angle .alpha. equal to
30.degree., and the difference between the frequencies F.sub.1 and F.sub.2
will be equal to 46 Hz for a height h equal to 0.5 meters (m).
Because of the small values of the frequencies F.sub.1 and F.sub.2, the
first and second spectra S.sub.1 and S.sub.2 can be obtained very easily,
e.g. by the fast Fourier transform after digitizing the filtered signal
supplied to the first input 10a of the central unit 10.
Optionally, it is possible to avoid using a height sensor 11 by providing
for the beam 4 of the incident radar wave, or for a portion of said beam,
to include a direction 4a that is perpendicular to the ground 2 so that
the first frequency spectrum S.sub.1 presents a relatively large
characteristic peak P.sub.1 (.pi./2) corresponding to a very low frequency
F.sub.1 (.pi./2).
This peak corresponds to the angle a having a value equal to .pi./2, such
that from above equation (VII) it is possible to compute the height h of
the transmitter/receiver 5 above the ground 2 from the formula:
##EQU18##
The invention is not limited to the particular embodiment described above;
on the contrary it extends to all variants, and in particular:
those in which the two spectra S.sub.1 and S.sub.2 are determined
simultaneously, the radar transmitting and receiving simultaneously at two
different frequencies f.sub.1 and f.sub.2 and including filters enabling
the respective signals relating to each of the two frequencies f.sub.1 and
f.sub.2 to be separated;
those in which the speed v is determined not solely from one pair of
frequencies F.sub.1 and F.sub.2 corresponding to one pair of peaks P.sub.1
and P.sub.2 in the first and second spectra, but from a plurality of pairs
of frequencies F.sub.1, F.sub.2 corresponding to a plurality of pairs of
peaks in the two spectra, the computed value of the speed v then possibly
being the average of the various speed values v computed from each pair of
frequencies F.sub.1, F.sub.2 ; under such circumstances, it is also
possible to determine the height h simultaneously as the speed v on the
basis of different frequency pairs F.sub.1, F.sub.2, by solving the system
of equations that corresponds to the various equations (VII) and (VIII)
relating to the various frequencies F.sub.1, F.sub.2 : in other words it
is possible to compute an expression for the speed v that is independent
of the height h; and
those in which the frequencies F.sub.1, F.sub.2 used for computing the
speed v correspond more generally to singular points in the spectra
S.sub.1, S.sub.2, i.e. not only to peaks, but also possibly to minima, or
to any other characteristic points.
To limit spectrum occupancy, the sawtooth frequency modulation shown in
FIG. 3 may advantageously have sawteeth that are substantially
symmetrical, i.e. with non-vertical rising and falling slopes.
To facilitate modulation of the radar frequency, the modulation may be
sinusoidal, with the spectra being measured in the substantially linear
portions of the sinusoidal frequency variation curves (i.e. in the
vicinity of the points of inflection in said sinusoidal curves).
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